### 2009

Martino, Luca; Miguez, Joaquin

A Novel Rejection Sampling Scheme for Posterior Probability Distributions Inproceedings

In: 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 2921–2924, IEEE, Taipei, 2009, ISSN: 1520-6149.

Abstract | Links | BibTeX | Tags: Additive noise, arbitrary target probability distributions, Bayes methods, Bayesian methods, Monte Carlo integration, Monte Carlo methods, Monte Carlo techniques, Overbounding, posterior probability distributions, Probability density function, Probability distribution, Proposals, Rejection sampling, rejection sampling scheme, Sampling methods, Signal processing algorithms, signal sampling, Upper bound

@inproceedings{Martino2009,

title = {A Novel Rejection Sampling Scheme for Posterior Probability Distributions},

author = {Luca Martino and Joaquin Miguez},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4960235},

issn = {1520-6149},

year = {2009},

date = {2009-01-01},

booktitle = {2009 IEEE International Conference on Acoustics, Speech and Signal Processing},

pages = {2921--2924},

publisher = {IEEE},

address = {Taipei},

abstract = {Rejection sampling (RS) is a well-known method to draw from arbitrary target probability distributions, which has important applications by itself or as a building block for more sophisticated Monte Carlo techniques. The main limitation to the use of RS is the need to find an adequate upper bound for the ratio of the target probability density function (pdf) over the proposal pdf from which the samples are generated. There are no general methods to analytically find this bound, except in the particular case in which the target pdf is log-concave. In this paper we adopt a Bayesian view of the problem and propose a general RS scheme to draw from the posterior pdf of a signal of interest using its prior density as a proposal function. The method enables the analytical calculation of the bound and can be applied to a large class of target densities. We illustrate its use with a simple numerical example.},

keywords = {Additive noise, arbitrary target probability distributions, Bayes methods, Bayesian methods, Monte Carlo integration, Monte Carlo methods, Monte Carlo techniques, Overbounding, posterior probability distributions, Probability density function, Probability distribution, Proposals, Rejection sampling, rejection sampling scheme, Sampling methods, Signal processing algorithms, signal sampling, Upper bound},

pubstate = {published},

tppubtype = {inproceedings}

}

Martino, Luca; Miguez, Joaquin

An Adaptive Accept/Reject Sampling Algorithm for Posterior Probability Distributions Inproceedings

In: 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, pp. 45–48, IEEE, Cardiff, 2009, ISBN: 978-1-4244-2709-3.

Abstract | Links | BibTeX | Tags: adaptive accept/reject sampling, Adaptive rejection sampling, arbitrary target probability distributions, Computer Simulation, Filtering, Monte Carlo integration, Monte Carlo methods, posterior probability distributions, Probability, Probability density function, Probability distribution, Proposals, Rejection sampling, Sampling methods, sensor networks, Signal processing algorithms, signal sampling, Testing

@inproceedings{Martino2009b,

title = {An Adaptive Accept/Reject Sampling Algorithm for Posterior Probability Distributions},

author = {Luca Martino and Joaquin Miguez},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5278644},

isbn = {978-1-4244-2709-3},

year = {2009},

date = {2009-01-01},

booktitle = {2009 IEEE/SP 15th Workshop on Statistical Signal Processing},

pages = {45--48},

publisher = {IEEE},

address = {Cardiff},

abstract = {Accept/reject sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. These samples are either accepted or rejected depending on a test involving the ratio of the target and proposal densities. In this paper we introduce an adaptive method to build a sequence of proposal pdf's that approximate the target density and hence can ensure a high acceptance rate. In order to illustrate the application of the method we design an accept/reject particle filter and then assess its performance and sampling efficiency numerically, by means of computer simulations.},

keywords = {adaptive accept/reject sampling, Adaptive rejection sampling, arbitrary target probability distributions, Computer Simulation, Filtering, Monte Carlo integration, Monte Carlo methods, posterior probability distributions, Probability, Probability density function, Probability distribution, Proposals, Rejection sampling, Sampling methods, sensor networks, Signal processing algorithms, signal sampling, Testing},

pubstate = {published},

tppubtype = {inproceedings}

}

Miguez, Joaquin; Maiz, Cristina S; Djuric, Petar M; Crisan, Dan

Sequential Monte Carlo Optimization Using Artificial State-Space Models Inproceedings

In: 2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, pp. 268–273, IEEE, Marco Island, FL, 2009.

Abstract | Links | BibTeX | Tags: Acceleration, Cost function, Design optimization, discrete-time dynamical system, Educational institutions, Mathematics, maximum a posteriori estimate, maximum likelihood estimation, minimisation, Monte Carlo methods, Optimization methods, Probability distribution, sequential Monte Carlo optimization, Sequential optimization, Signal design, State-space methods, state-space model, Stochastic optimization

@inproceedings{Miguez2009,

title = {Sequential Monte Carlo Optimization Using Artificial State-Space Models},

author = {Joaquin Miguez and Cristina S Maiz and Petar M Djuric and Dan Crisan},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4785933},

year = {2009},

date = {2009-01-01},

booktitle = {2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop},

pages = {268--273},

publisher = {IEEE},

address = {Marco Island, FL},

abstract = {We introduce a method for sequential minimization of a certain class of (possibly non-convex) cost functions with respect to a high dimensional signal of interest. The proposed approach involves the transformation of the optimization problem into one of estimation in a discrete-time dynamical system. In particular, we describe a methodology for constructing an artificial state-space model which has the signal of interest as its unobserved dynamic state. The model is ädapted" to the cost function in the sense that the maximum a posteriori (MAP) estimate of the system state is also a global minimizer of the cost function. The advantage of the estimation framework is that we can draw from a pool of sequential Monte Carlo methods, for particle approximation of probability measures in dynamic systems, that enable the numerical computation of MAP estimates. We provide examples of how to apply the proposed methodology, including some illustrative simulation results.},

keywords = {Acceleration, Cost function, Design optimization, discrete-time dynamical system, Educational institutions, Mathematics, maximum a posteriori estimate, maximum likelihood estimation, minimisation, Monte Carlo methods, Optimization methods, Probability distribution, sequential Monte Carlo optimization, Sequential optimization, Signal design, State-space methods, state-space model, Stochastic optimization},

pubstate = {published},

tppubtype = {inproceedings}

}